Nihonkai Mathematical Journal

Garden Representation and Interior Variation of Real Rational Functions

Sayaka Tamae

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In this paper, we show that the fundamental surgeries of the graph representation for real rational functions can be achieved by classical interior variations essentially due to Schiffer. As an application we give a constructive proof of the main theorem of Natanzon, Shapiro and Vainshtein in [2].

Article information

Nihonkai Math. J., Volume 22, Number 1 (2011), 39-47.

First available in Project Euclid: 14 June 2012

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Zentralblatt MATH identifier

Primary: 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10} 26C15: Rational functions [See also 14Pxx] 32G05: Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]

Real rational functions interior variation


Tamae, Sayaka. Garden Representation and Interior Variation of Real Rational Functions. Nihonkai Math. J. 22 (2011), no. 1, 39--47.

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  • Y. Imayoshi and M.Taniguchi, An introduction to Teichmüller spaces, Springer-Verlag, 1992.
  • S. Natanzon, B. Shapiro and A. Vainshtein, Topological classification of generic real rational functions, J. Knot Theory Ramifications, 11 (2002), 1063–1075.
  • M. Schiffer and D. C. Spencer, Functions of finite Riemann surfaces, Princeton Univ. Press, 1954.
  • M. Taniguchi, Period-preserving variation of a Riemann surface, Kodai Math. Journ., 16 (1993), 487–493.